Since log-Sobolev inequalities are preserved under bounded perturbations
by [1]}'s theorem, we provide our extended
results through convexification of non-convex domain [2]}, [3]}.
Convexification of non-convex domain is an original approach proposed
by [2]}, [3]}, developed and apply to
strongly convex outside a compact set by [3]}.
We would like to emphasize that it is non trivial to apply their results
in our case since the requirement of strong convexity. Before starting
our extension, we need an additional lemma, taken from [2]}, [3]},
for our proof.
